periodic table: why the repetition

Periodic Table: Why the repetition

• The periodic table is the most important organizing principle in chemistry.

• Chemical and physical properties of elements in the same group are similar.

• All chemical and physical properties vary in a periodic manner, hence the name periodic table.

For instance, hydrogen, lithium, sodium, and potassium, were all known to make chlorides in a 1:1 mole ratio. The “wrapping around” of the periodic table was done to capture these similarities into columns.

Periodic Table

Most tables in your book (other than the periodic table) look nothing like the periodic table. Instead they are a few columns of data. The periodic table, done this way, would look like this:

Hydrogen 1.00794

Helium 4.002602

Lithium 6.941

Beryllium 9.012181

Boron 10.811

Carbon 12.0107etc.

Notice that the actual periodic table does not uniformly order the elements by atomic mass. (Compare argon to potassium.)

So how did we get the atomic numbers?

•The atomic masses are

clearly pretty good guides

(almost perfect, in fact)

•In 1913, an English

spectroscopist H.G.J. Moseley

performed a series of x-ray

experiments with the

following data:

Periodic Table: Predictions

Periodic Table: Microscopic Explanation

The whole rest of the chapter is generally about developing this explanation.

•The proton and the electron were the two sub-atomic particles known, so the explanation had to involve them somehow.

•But Moseley showed the protons uniformly increase as you go along the periodic table; they don’t behave periodically.

•So the electrons must be explanation.

•This makes sense: electrons are the outer part of the atom. Any time two atoms meet, the electrons meet first, So they should be most important in how two atoms interact.

Periodic Electron Behavior

Electromagnetic Radiation

• Frequency (, Greek nu):

Number of peaks that pass a

given point per unit time.

• Wavelength (, Greek lambda):

Distance from one wave peak

to the next.

• Amplitude: Height measured from the center of the wave. The square of the amplitude gives intensity.

Electromagnetic Spectrum

Electromagnetic Spectrum: Math

• Speed of a wave is the wavelength (in meters) multiplied by its frequency in reciprocal seconds.

– Wavelength x Frequency = Speed

– (m) x (s–1) = c (m/s–1)

Atomic Spectra: Line spectra•Line spectra: run the emitted light through a monochromator. very distinctive results. Called “atomic fingerprints.”

Atomic Spectra: Hydrogen spectrum “explained”

22

1

2

11

nR

Works for all n integers (getting weaker are n increases).R is now called Rydberg constant.

Balmer showed:

Rydberg showed it could be generalized to:

22

111

nmR

For all n>m

Sadly, this equation only worked for one-electron systems like H or He+ or Li2+. Many tried to generalize the equation for many-electron systems. All attempts failed.

The state of affairs in ~1900:•A mathematical description of the hydrogen atom spectrum was available, but it had no physical basis. (That is, there was no real “why”.)

•There were two kinds of “things” in the universe: particles and waves

•Particles come in discrete chunks that can be counted. That is, they are quantized. They carry energy as kinetic energy which is infinitely adjustable.

•Waves do not come in discrete chunk but instead are continuous and thus are not countable like particles. They are not quantized. They have wavelengths (or frequencies) that are infinitely adjustable. They carry energy that is measurable as the intensity of the wave. How waves carry energy is unknown.

•Phenomena yet to be explained:•Blackbody radiation•Photoelectric effect•How the atom works

Blackbody radiationWhen a metal chunk is resistively heated to a high enough temperature,It starts to glow.

This glow depends only on the temperature and not on the material.

The wavelengths of light emitted decrease as the temperature increases, starting first down in the microwave and infra-red region and sliding through the visible from red to violet, and then into the ultraviolet.

Classically, blackbodies emit light at the frequency they vibrate. Because most of the atoms are highly constrained, most should vibrate very quickly and thus emit high frequency light, but in truth most emit low frequency light.

• Blackbody radiation is the visible glow that objects with unbound electrons emit when heated.

• Max Planck (1858–1947): proposed that energy is only emitted in discrete packets called quanta.

• The amount of energy depends on the frequency:

E h

hc h 6.626 10 34 J s

Waves as Particles:Quantized Energy

Blackbodies explainedAt the time Planck’s solution was considered a mathematical oddity. That is, he had found an equation that had the same shape as the experimental blackbody curves, but the explanation behind the equation was all wrong.

In fact, Planck never fully embraced quantum theory and doubted the work of Einstein and others for the rest of his life.

But the key ideas were now out there:light comes in discrete chunksthe energy of light is related to its frequency and not to its amplitudethe energy of these chunks of light could not be just any value

Photoelectric EffectIf you put a piece of metal in a vacuum tube, and then shine light of certain frequency on it, the metal emits electrons. This is called the photoelectric effect. Experimentally it was found that the light had to be of a high enough frequency or no electrons would be emitted. And as the light increased in frequency above this “threshhold frequency” the kinetic energy of the electrons increased.

Classically, electrons oscillate at the frequency of the incoming light. And the higher the amplitude of the oscillating light, the bigger the amplitude of the electron’s oscillations. Thus any frequency of light should be able to make a metal emit electrons, and the kinetic energy should vary only as the intensity of the light increases.

Waves as Particles: Quantized Energy

• Albert Einstein (1879–1955): • Used the idea of

quanta to explain the photoelectric effect.

• He proposed that light behaves as a stream of particles called photons.

Waves as Particles:Quantized Energy

• A photon’s energy must exceed a minimum threshold for electrons to be ejected.

• Energy of a photon depends only on the frequency.

Photoelectric Effect ExplainedWhen Einstein solved his equations to fit the experimental photoelectric effect data, he found that the photons must be carrying energy in multiples of 6.626*10-34 J s. This was exactly the constant that Planck found with entirely different experiments!

At this point, this quantum theory of light was taken much more seriously. While many doubters remained for decades to come, most reasoned that the presence of the same constant (found independently) showed that there must be something real behind the theory.

But still this does not explain the atom.

Particles as Waves: de Broglie wavelengths

• Louis de Broglie (1892–1987): Suggested waves

can behave as particles and particles can

behave as waves. This is called wave–particle

duality. For Light : h

mc

h

p

For a Particle : h

mv

h

p

Rydberg and the Atom: Bohr Model

Heisenberg Uncertainty Principle

• Werner Heisenberg (1901–1976): Showed that it is impossible

to know (or measure) precisely both the position and velocity

(or the momentum) at the same time.

• The simple act of “seeing” an electron would change its energy

and therefore its position.

Heisenberg Uncertainty Principle

)()4()( : position selectron' iny Uncertaint

4))(( :lety Princip UncertainHeisenberg

mv

hx

hmvx

• Wave functions describe the behavior of electrons.

• Each wave function contains four variables called quantum

numbers. Quantum numbers must be integers. (That is, they

are quantized.) The three we need now are:

– • Principal Quantum Number (n)

– • Angular-Momentum Quantum Number (l)

– • Magnetic Quantum Number (ml)

Electron wave functions

Principal Quantum Number (n)

• Principal Quantum Number (n): Defines the size and energy level of the orbital. n = 1, 2, 3,

• As n increases, the electrons get farther from the nucleus.

• As n increases, the electrons’ energy increases.

• Each value of n is called a shell.

Angular Momentum (l)

•Angular-Momentum Quantum Number (l): Defines the three-dimensional shape of the orbital.

•For an orbital of principal quantum number n, the value of l can have an integer value from 0 to n – 1.

•This gives the subshell notation:l = 0 = s orbital l = 1 = p orbital

l = 2 = d orbital l = 3 = f orbital l = 4 = g orbital

Magnetic Quantum Number (ml)

•Magnetic Quantum Number (ml): Defines the spatial orientation of the orbital.

•For orbital of angular-momentum quantum number, l, the value of ml has integer values from –l to +l.

•This gives a spatial orientation of:

l = 0 giving ml = 0

l = 1 giving ml = –1, 0, +1

l = 2 giving ml = –2, –1, 0, 1, 2, and so on…...

Quantum Numbers

Orbitals and Energy

Electron Positions

• s Orbital Shapes:

Electron Positions (II)

• p Orbital Shapes:

Electron Positions (III)

• d and f Orbital Shapes:

What are orbitals?

•Orbitals (and shells & subshells) are equations (fundamentally). They are four-dimensional equations that solve the Schrodinger equation.

•They are theoretical entities.

•Two questions:•What do orbitals represent?•What experimental evidence do we have to support them?

What are orbitals?

•Orbitals can be considered in two ways:

•1. Orbitals represent the “cage” in which the electron resides. The calculated probabilities represent the “pacing of the tiger in the cage.”

•2. Orbitals represent the electron itself. In the atom the electron has a wave-like existence and the orbital is the spatial area over which the wave has non-zero amplitude. The electron has no fixed shape.

What experimental evidence?

How do atoms use shells, subshells, and orbitals?They use shells, subshells, and orbitals to organize

electrons.

Why do atoms organize electrons?They organize electrons in order to minimize the

energy.

So to find evidence of shells, subshells, and orbitals we need to measure the energies of electrons in the atom.

Experimental Evidence:Shells

Ionization Energy (IE) ExperimentX-ray (h)

e-

h – KE(e-) = IE

KE detector

Only capable of seeing the most easily removed electron (1IE). We can rejigger the experiment to see 2IE, 3IE, etc.

We also cannot see how many electrons come off.

What Determines theElectron’s Energy?

Proximity to the nucleusThe closer to the nucleus, the lower the

electron’s energy (and therefore the higher the ionization energy of the electron.)

The greater the number of protons in the nucleus, the greater the attraction is going to be.

What should IE vs. Z look like?

• What should IE depend on?

• As Z increases, what if the new electron is placed randomly?

• As Z increases, what if new electron is placed in same shell?

• As Z increases, what if each electron is placed further away from nucleus?

• Any other possibilities to be considered?

IE Experiment Actual Data

Evidence for Subshells: PES experiments

The PES experiment works rather like the IE experiment, but is more subtle.It allows one to see the energy at which each of the electrons comes off (not just the easiest one), and how many electrons come off at each energy.

We are still making ions.

PES Data (Hydrogen)

Higher ionization energies to the left, so electrons that are further from the nucleus are to the right

The most easily removed electrons from the PES data must match the IE expt. data

The number of electrons coming off is shown by the height of the peak

PES Data (Hydrogen and Helium)

PES Data (H – Li)Two different shells show as two peaks with a big gap between them

PES Data (H – Be)

PES Data (H – B)

Two subshells in the same shellTwo different shells

PES Data (B – Ne)

So apparently, the way the system works is that we completely fill a subshell and then move on to the next subshell, completely filling it, until there are no more subshells in a shell and then we move on to the next shell.

PES Data (MJ/mol)Element 1st peak 2nd peak 3rd peak

H 1.31 (1)

He 2.37 (2)

Li 6.26 (2) 0.52 (1)

Be 11.5 (2) 0.90 (2)

B 19.3 (2) 1.36 (2) 0.80 (1)

C 28.6 (2) 1.72 (2) 1.09 (2)

N 39.6 (2) 2.45 (2) 1.40 (3)

O 52.6 (2) 3.12 (2) 1.31 (4)

F 67.2 (2) 3.88 (2) 1.68 (5)

Ne 84.0 (2) 4.68 (2) 2.08 (6)

PES Data (Na – Sc)Element 1st peak 2nd peak 3rd peak 4th peak 5th peak 6th peak 7th peak

Na 104 (2) 6.84 (2) 3.67 (6) 0.50 (1)

Mg 126 (2) 9.07 (2) 5.31 (6) 0.74 (2)

Al 151 (2) 12.1 (2) 7.79 (6) 1.09 (2) 0.58 (1)

Si 178 (2) 15.1 (2) 10.3 (6) 1.46 (2) 0.79 (2)

P 208 (2) 18.7 (2) 13.5 (6) 1.95 (2) 1.01 (3)

S 239 (2) 22.7 (2) 16.5 (6) 2.05 (2) 1.00 (4)

Cl 273 (2) 26.8 (2) 20.2 (6) 2.44 (2) 1.25 (5)

Ar 309 (2) 31.5 (2) 24.1 (6) 2.82 (2) 1.52 (6)

K 347 (2) 37.1 (2) 29.1 (6) 3.93 (2) 2.38 (6) 0.42 (1)

Ca 390 (2) 42.7 (2) 34.0 (6) 4.65 (2) 2.90 (6) 0.59 (2)

Sc 433 (2) 48.5 (2) 39.2 (6) 5.44 (2) 3.24 (6) 0.77 (1) 0.63 (2)

1s 2s 2p 3s 3p 3d? 4s? 4s? 3d?

Subshell Filling Order• Filling order gets more

complicated as you get to the later subshells

• This happens because the electron-electron repulsion starts to affect the energies of the subshells pretty substantially

1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 7s 7p

Increasing Energy

[He][Ne] [Ar] [Kr] [Xe] [Rn]

Core

We have rules!!

Electron Configurations• Electron configurations label the shell and subshell of each

electron• We use the shell and subshell labels we know from quantum

mechanics• We use the populations we know from the PES experiments

Element 1st peak 2nd peak 3rd peak

H 1.31 (1)

He 2.37 (2)

Li 6.26 (2) 0.52 (1)

Be 11.5 (2) 0.90 (2)

B 19.3 (2) 1.36 (2) 0.80 (1)

C 28.6 (2) 1.72 (2) 1.09 (2)

N 39.6 (2) 2.45 (2) 1.40 (3)

O 52.6 (2) 3.12 (2) 1.31 (4)

F 67.2 (2) 3.88 (2) 1.68 (5)

Ne 84.0 (2) 4.68 (2) 2.08 (6)

Li: 1s2 2s1

F: 1s2 2s2 2p5

Why that particular filling order?

• Because it minimizes the energy? (But that just changes the question.)

Zeff and Subshell Energies

Electron Shielding

• Electrons repel each other• Electrons are attracted to the nucleus.• Orbitals with a low ℓ have a higher intensity of

their near the nucleus.

• This intensity, in effect, blocks electrons further out from feeling the full pull of the nucleus. This is called “electron shielding.”

Effective Nuclear Charge

• Electron shielding leads to energy differences among orbitals within a shell.

• Net nuclear charge felt by an electron is called the effective nuclear charge (Zeff).

• Zeff = Zactual – electron shielding

Effective Nuclear Charge

• Zeff is the observed attraction to the nucleus.

• Zeff is different for different subshells

• Zeff is lower than actual nuclear charge.

• Zeff increases toward nucleus ns > np > nd > nf

• This explains certain periodic changes observed.

Things we know

•The 1s subshell has the quantum numbers 1,0,0.•The 1s subshell has one orbital.•The 1s subshell holds two electrons.

•Every electron in a system needs to have different quantum numbers.

Umm, what gives?

Electron Spin

•Electrons need to have unique quantum number sets.

•Electrons have an additional spin quantum number ms

•So every different orbital (1st 3 quantum numbers) can hold two electrons, each with a different spin quantum number.

Pauli Exclusion Principle

The Pauli Exclusion Principle states that no two electrons (in any one atom) have the same four quantum numbers.

Electron Configuration Principles: Aufbau Principles

• In the atom’s most stable state, the electrons in the atom are in

the lowest energy orbital possible.

• Pauli Exclusion Principle: No two electrons in an atom can have

the same quantum numbers (n, l, ml, ms).

• Hund’s Rule: When filling orbitals in the same subshell,

maximize the number of parallel spins.

How does electron spin affect electron energy?

•For a single electron alone in space, spin doesn’t affect the energy at all.

•Spin affects the energy of two electrons interacting with each other.•Electrons with the same spin have slightly lower energy than electrons with opposite spin.

•Because electrons have the same charge, putting them in different locations (different orbitals) lowers the energy substantially.

•Together, these are the basis of Hund’s rule.

Orbital Diagrams

We now can write true electron configurations (showing which electrons are in which orbital.)

Ironically, this is not done in orbital diagrams (rather than in electron configurations, which we will make with only shells and subshells labeled.) In orbital diagrams we represent each orbital in each subshell as a box or line. We represent each electron as an arrow pointing up or down (representing the two different spins.)

Orbital Diagrams vs. Electron Configurations

Li 1s2 2s1

1s 2s

Be 1s2 2s2

1s 2s

B 1s2 2s2 2p1

1s 2s 2p

C 1s2 2s2 2p2

1s 2s 2p

Can we see evidence for this effect?YES!

We see it in the unexpectedly low IE of sulfur and oxygen.

Electron Configuration Principles

• Rules of Aufbau Principle:

1. Lower n orbitals fill first.

2. Each orbital holds two electrons; each with different ms.

3. Half-fill degenerate orbitals before pairing electrons.

Writing Electron Configurations

• Configurations are written as collections of subshells.• Start with the lowest energy orbitals and continue in

increasing energy order.• The number of electrons in that subshell is written as

a superscript to the right of the subshell label.• It is acceptable to abbreviate configurations by

putting the previous noble gas in brackets and continuing from there.

Electron Configurations and the Periodic Table

Ground State vs. Excited State

• The electron configurations we have produced so far are all ground state configurations.

• If all the electrons are in proper orbitals (properly), but the filling has not obeyed the Aufbau principle, it is an excited state configuration.

Which principles obeyed for excited states (and ground states)?

• Only 2 electrons per orbital• 2 electrons in an orbital must have opposite

spin

Which principles not obeyed for excited states?

• Parallel spins unnecessary• Filling subshells unnecessary

Anomalous Electron Configurations

•Electrons and atoms do not have attitudes. Whatever they do they do to lower the energy of the atom.

•What lowers the energy?•All full shells lowers the energy a LOT•All full subshells lowers the energy somewhat•All parallel spins lowers the energy a little, but it increases as the number of parallel spins increases

Anomalous Electron Configurations

• Anomalous Electron Configurations: Result from unusual stability of half-filled & full-filled subshells.

• Chromium should be [Ar] 4s2 3d4, but is [Ar] 4s1 3d5

• Copper should be [Ar] 4s2 3d9, but is [Ar] 4s1 3d10

• In the second transition series this is even more pronounced,

with Nb, Mo, Ru, Rh, Pd, and Ag having anomalous

configurations (Figure 5.20).We’ve already seen this increased stability. Where?

Atomic Radius•As you move down a group the atomic size becomes bigger as new shells of electrons become populated.

•As you move rightward across a group the atomic size generally becomes smaller as the effective nuclear charge grows (because the new electrons are in the same subshell as the previous electrons).